Factorization of Block Triangular Matrix Functions in Wiener Algebras on Ordered Abelian Groups
Cornelis V. M. van der Mee, Leiba Rodman, Ilya M. Spitkovsky, Hugo J. Woerdeman · Birkhäuser Basel eBooks · 2004
The notion of Wiener-Hopf type factorization is introduced in the abstract framework of Wiener algebras of matrix-valued functions on connected compact abelian groups. Factorizations of 2 x 2 block triangular matrix functions with elementary functions on the main diagonal are studied in detail. A conjecture is formulated concerning characterization of dual groups with the property that every invertible matrix function in a Wiener algebra admits a factorization. Applications of factorization are given to systems of difference equations and orthogonal families of functions. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.